Spectral Analysis of Random Sparse Matrices
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- ANDO Tomonori
- Canon Inc.
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- KABASHIMA Yoshiyuki
- Dept. of Comp. Intelligence and Systems Science, Tokyo Institute of Technology
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- TAKAHASHI Hisanao
- Tokai University and Tokyo Institute of Technology
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- WATANABE Osamu
- Dept. of Math. and Comp. Sciences, Tokyo Institute of Technology
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- YAMAMOTO Masaki
- Department of Informatics, Kwansei-Gakuin University
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Abstract
We study n×n random symmetric matrices whose entries above the diagonal are iid random variables each of which takes 1 with probability p and 0 with probability 1-p, for a given density parameter p=α/n for sufficiently large α. For a given such matrix A, we consider a matrix A' that is obtained by removing some rows and corresponding columns with too many value 1 entries. Then for this A', we show that the largest eigenvalue is asymptotically close to α+1 and its eigenvector is almost parallel to all one vector (1,...,1).
Journal
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- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A (6), 1247-1256, 2011
The Institute of Electronics, Information and Communication Engineers
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Details 詳細情報について
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- CRID
- 1390001206310288896
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- NII Article ID
- 10029802201
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- NII Book ID
- AA10826239
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- ISSN
- 17451337
- 09168508
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed